Chapter 13, Problem 50P

(a)

To determine

Time 0 ATCFs for existing asset and new asset.

Answer to Problem 50P

Time 0 ATCF for existing asset is $28,875.

Time 0 ATCF for new asset is $76,500.

Explanation of Solution

Old asset

  $\begin{array}{c}\text{Annual depreciation }=\frac{\text{Total}\text{cost}-\text{Salvage}\text{Value}}{\text{Years}}\\ =\frac{50000-15000}{10}\\ =\$3,500\end{array}$

  $$

  $\begin{array}{c}\text{Book Value as at today} =50000-3500\times 7\\ =\$25500\end{array}$

  $\begin{array}{c}\text{ATCF for Old asset}=30000–\left(30000-25500\right)\times 25\%\\ =\$28,875\end{array}$

New asset

New asset is entitled to 10% investment tax credit, hence ATCF at Time 0 for new asset will be as follows:

  $\begin{array}{c}\text{ATCF }=\text{ First cost}–10\%\text{investment tax credit} \\ =85000–10\%\times 85000 \\ =\$76,500\end{array}$

(b)

To determine

Time 0 ATCFs for existing asset and new asset if present market value of existing asset is $25,500.

Answer to Problem 50P

Time 0 ATCF for existing asset is $25,500.

Time 0 ATCF for new asset is $76,500.

Explanation of Solution

Old asset

  $\begin{array}{c}\text{Annual depreciation}=\frac{\text{Total}\text{cost}-\text{Salvage}\text{Value}}{\text{Years}}\\ =\frac{50000-15000}{10}\\ =\$3,500\end{array}$

  $$

Book Value as at today = $50000-3500\times 7$

= $25500

  $\begin{array}{c}\text{ATCF for Old asset}=25500–\left(25500-25500\right)\times 25\%\\ =\$25,500\end{array}$

New asset New asset is entitled to 10% investment tax credit, hence ATCF at Time 0 for new asset will be as follows:

  $\begin{array}{c}\text{ATCF }=\text{ First cost }–10\%\text{ investment tax credit }\\ =85000–10\%85000 \\ =\$76,500\end{array}$

(c)

To determine

Time 0 ATCFs for existing asset and new asset if present market value of existing asset is $18,000.

Answer to Problem 50P

Time 0 ATCF for existing asset is $19,875.

Time 0 ATCF for new asset is $76,500.

Explanation of Solution

Old asset

  $\begin{array}{c}\text{Annual depreciation}=\frac{\text{Totalcost}-\text{SalvageValue}}{\text{Years}}\\ =\frac{50000-15000}{10}\\ =\$3,500\end{array}$

  $$

  $\begin{array}{c}\text{Book Value as at today}=50000-3500\times 7\\ =\$25500\end{array}$

  $\begin{array}{c}\text{ATCF for Old asset}=18000–\left(18000-25500\right)\times 25\%\\ =\$19,875\end{array}$

New asset New asset is entitled to 10% investment tax credit, hence ATCF at Time 0 for new asset will be as follows:

  $\begin{array}{c}\text{ATCF }=\text{ First cost }–10\%\text{ investment tax credit } \\ =85000–10\%\times 85000 \\ =\$76,500\end{array}$